Chapter 3
Numerical differentiation
3.1 Introduction
Numericai integration and differentiation are some of the most frequently needed methods in compu
tationai physics. Quite often we are confronted with the need of evaiuating either f or an integrai
f f(

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Practical Points Concerning the Solution of the-Schrodinger Equ

I ' ravparlment, Notheaswm University, Boston Mas
Work 14 July 1980; accepted 3 September 1980
_ problem and . . ,
:mespace-lhng orbits. In this new
w energy and the energy after i:
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magnum of Functions
4.
Lb
' omitted. However. if you an: '
4.5. below, and phase m unt/0(3). and you dont know the WW.
. - - - function . a
"m'ass'cal 2"?th the associated set of onhogonal polynomials 1; no. 1 inc
. V
b . the construct: . . m.
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Chapter 11
Quantum Monte Carlo methods
If, in some cataclysm, all scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most
information in the fewest words? I beli

The physics behind path integrals in quantum mechanics
Philip D. Mannheim
Department of Physics, University of Connecticut, Storrs, Connecticut 06268
(Received 29 September 1981; accepted for publication 4 May 1982)
We present a simple pedagogical discuss

Chapter 8
Outline of the Monte-Carlo strategy
Iacta Alea est, the die is cast, is what Julius Caesar is reported by Suetonius to have
said on January 10, 49 BC as he led his army across the River Rubicon in Northern Italy.
(Twelve Ceasars)Gaius Suetonius

Chapter 9
Random walks and the Metropolis
algorithm
Nel mezzo del cammin di nostra vita, mi ritrovai per una selva oscura, ch la diritta via
era smarrita. (Divina Commedia, Inferno, Canto I, 1-3)Dante Alighieri
The way that can be spoken of is not the con

Application of Shooting Method to Solve the Schrdinger Equation
Reis, Vtor Eullio - Nusp 8636309
IFSC - University of So Paulo
Av. Trabalhador So Carlense, 400
So Carlos, So Paulo
The Shooting Algorithm
Abstract
In this work the numerical solution of the

Chapter 8
Differential equations
If God has made the world a perfect mechanism, he has at least conceded so much to our imperfect
intellect that in order to predict little parts of it, we need not solve innumerable differential equations,
but can use dice

Chapter 12
Eigensystems
12.1 Introduction
Together with linear equations and least squares, the third major problem in matrix computations deals
with the algebraic eigenvalue problem. Here we limit our attention to the symmetric case. We focus in
particul

Chapter 9
Two point boundary value problems
Abstract When differential equations are required to satisfy boundary conditions at more
than one value of the independent variable, the resulting problem is called a boundary value
problem. The most common case

45 CHAPTER 2. INTRODUCTION TO MONTE CARLO
2:0 : wzbc and is
i b2
9(e3) : a. m :4;-
Writing:
W 2 2 E: d.
9(a) as: ~ me) + a g 2,
we hdve expressed the polynomial as the sum of two positive denite functions with
the second in the form of a probability times

Assignment IV: Simulation of the Boltzmann distribution
Due 11/07/2016
The homework problem consists of the entire Physics project 9.6, p. 224 from M. HjorthJensen Chapter 9.

Assignment VIII: Monte Carlo Integration
Due 10/31/2016
1. Multi-Dimensional Integration
Using Monte-Carlo integration evaluate the 10-dimensional integral
I=
Z
0
1
dx1
Z
0
1
dx2
Z
0
1
dx10 (x1 + x2 + + x10 )3 .
(1)
(a) Conduct 16 trials and take the ave

Assignment XI: Differential Equations
Due 11/21/2016
1. (6 pts) Solution of a Differential Equation
(a) Writer a computer code to solve the differential equation
y (x) = 2(y + 1)
(1)
in the region 2 < x < 2 using Eulers method. Use as initial condition y(

Assignment VII: Randomness
Due 10/24/2016
1. Random Sequences
(a) Write a simple program to generate random numbers using the linear congruent
method, defined by
ri (ari1 + c)modM.
(1)
The built-in function mod is called with 2 arguments: mod (a,M).
(b) F

Physics 115/242
Numerov method for integrating the one-dimensional Schr
odinger equation.
Peter Young
The one-dimensional time-independent Schr
odinger equation is
h
2 d2
+ V (x)(x) = E(x),
2m dx2
(1)
where (x) is the wavefunction, V (x) is the potentia

Assignment XII: Boundary Value Problems
Due 11/29/2016
1. (6 pts) Consider the same 3D harmonic oscillator as in problem 2 of Homework 6.
1. Set up a boundary value differential equation to solve for l = 0 and u(). Use either
the Runge-Kutta 4th order cod

Assignment X: Applications of the Metropolis Algorithm
Due 11/14/2016
1. Lattice Path Integration
(a) Solve the ground state probability for the 1D Harmonic Oscillator via Feynman path
integration using the Metropolis algorithm following the implementatio

1 Essential Emacs
To start an emacs editing session, type: emacs [le]. If you want the graphical features
of emacs and work on it remotely, be sure to set the DISPLAY by setenv (in C shell)
or export (in Korn and BASH shell) at rst. If you log in remotely

Assignment I: First Steps and 2D Plots
Due 8/29/2016
1. Plot functions:
1. Bessel function
sin x
(1)
x
for x [0, 10]. Write a code to create your data input file for xmgrace and take
special care for x 0.
j0 (x) =
2. Legendre function of the second kind
1

Assignment II: Errors in Computing, Recursion Relations, and Roots
Due 9/12/2015
There are few simple but golden rules to create programs that build a useful code library.
Thus some hints for good coding:
Write small modules (routines/functions); avoid b

Chapter 2
Introduction to C+ and Fortran
Abstract This chapters aims at catching two birds with a stone; to introduce to you essential
features of the programming languages C+ and Fortran with a brief reminder on Python
specific topics, and to stress prob

Assignment IV: Numerical Quadrature
Due 9/26/2016
1.Evaluate the following integral numerically:
=
Z 1
dx
1
2
1 + x2
(1)
using Trapezoidal, Simpson and Gaussian quadrature.
Modify the program integ1.f90 for this part of the homework.
Compare the relative

Chapter 1
Introduction
In the physical sciences we often encounter problems of evaluating various properties of a
given function f (x). Typical operations are differentiation, integration and finding the roots of
f (x). In most cases we do not have an ana

SUSE Desktop Environment
Ch. Elster
August 16, 2016
Abstract
SUSE 13.x Desktop Guide 101
Kickoff Application Launcher
To find application, go to the Suse Icon for the application launcher in
the lower left corner. The second tab Applications will take you

Assignment V : Data Fitting
Due 10/03/2016
1. Polynomial Interpolation
Consider the data set for a neutron cross section given in crossX2.dat.
(a) Use the Lagrange interpolation formula of Eq. (5.3) (R.H. Landau, 1st edition or
subsection 9.1.2 2nd editio

Assignment VI: Eigensystems
Due 10/17/2016 (4 pm)
1. Testing Matrix Calls (partially in Class)
Before using subroutines from external libraries such as lapack or linpack, it is a good idea
to test those routines with small matrices, for which you know the

Useful Commands for Getting Around I
In the Computer Lab all computers on the right hand side from the isle run SUSE Linux.
Essentially all your work should be done on one of those. If you use your private computer
you need to make sure that all your code